ASYMPTOTIC VALUES AND THE GROWTH OF ANALYTIC FUNCTIONS IN SPIRAL DOMAINS

ASYMPTOTIC VALUES AND THE GROWTH OF ANALYTIC FUNCTIONS IN SPIRAL DOMAINS

In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ∂̄-mollification and may be of use in other problems as well.

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Veröffentlicht in:Publicacions matemàtiques 1993-01, Vol.37 (2), p.465-477
Hauptverfasser: Brennan, J. E., Volberg, A. L.
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Asymptotic value
Comportamiento asintótico
Funciones analíticas
Función subarmónica
Mathematical functions
Mathematical growth
Mathematical inequalities
Mathematical theorems
Subharmonics
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Zusammenfassung:In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ∂̄-mollification and may be of use in other problems as well.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_37293_16